Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
350 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #31827279 | C2 | semidirect |
| 2. #31827278 | C2 | semidirect |
| 3. #31826908 | C2 | semidirect |
| 4. #31826907 | C2 | semidirect |
| 5. #31826904 | C2 | semidirect |
| 6. #31826896 | C2 | semidirect |
| 7. #31826895 | C2 | semidirect |
| 8. C2×#22583556 | C2 | semidirect |
| 9. Q32×D283 | C2 | semidirect |
| 10. #31826883 | C2 | semidirect |
| 11. #510×C283 | C2 | semidirect |
| 123. C283 | #3417 | semidirect |
| 130. #510 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827279 | 2 |
| #31827278 | 2 |
| #31826908 | 2 |
| #31826907 | 2 |
| #31826904 | 2 |
| #31826896 | 2 |
| #31826895 | 2 |
| C2×#22583556 | 2 |
| Q32×D283 | 2 |
| #31826883 | 2 |
| #510×C283 | 2 |
| #3417 | 283 |